Based on your requirements, there are several payment systems that you can consider for your service:
1. Stripe: Stripe is a popular payment system that provides access to a pay API. It allows customers to specify the sum they want to pay and supports refunds. However, please note that the minimum refund period may vary depending on your business settings. Stripe also supports withdrawal to Payoneer cards and integrates with PayPal.
2. PayPal: PayPal is a well-known payment system that supports both API access and customer-specified payments. It offers refund capabilities and supports withdrawals to Payoneer cards. Since PayPal is desirable for you, it could be a suitable option if you choose to integrate the PayPal API directly.
3. Braintree: Braintree is another payment system that provides API access and supports customer-specified payments. It has built-in refund functionality and integrates with PayPal. However, please check whether Braintree supports withdrawals to Payoneer cards, as this may vary depending on the specific integration.
Here are a few more payment systems that you can consider:
1. Square: Square is a payment system that provides API access and allows customers to specify the amount they want to pay. It offers refund capabilities, and while it may not have direct integration with Payoneer, you can explore options to transfer funds from Square to your Payoneer account using other methods.
2. Authorize.Net: Authorize.Net is a widely-used payment gateway that supports API access and customer-specified payments. It offers refund functionality and integrates with PayPal. While it may not have direct integration with Payoneer, you can explore options to transfer funds from Authorize.Net to your Payoneer account.
3. 2Checkout: 2Checkout is a global payment platform that provides access to an API and supports customer-specified payments. It offers refund capabilities and has integration with PayPal. While it does not explicitly mention Payoneer on their website, you can reach out to their support team to inquire about possible integration options.
few more payment systems that you can consider:
1. Adyen: Adyen is a global payment platform that offers API access and allows customers to specify payment amounts. It supports refunds and provides integration with PayPal. While it does not explicitly mention Payoneer on their website, you can contact their support team to inquire about the possibility of withdrawing funds to Payoneer.
2. Worldpay: Worldpay is a payment processing company that offers API access and supports customer-specified payments. It provides refund capabilities and integrates with PayPal. While Worldpay does not mention direct integration with Payoneer, you can explore options to transfer funds from Worldpay to your Payoneer account using other methods.
3. PayU: PayU is a leading online payment service provider that offers API access and supports customer-specified payments. It provides refund functionality and integrates with PayPal. While it may not have direct integration with Payoneer, you can reach out to their support team for more information on whether you can withdraw funds to a Payoneer card.